Computers & Mathematics with Applications

Published by Elsevier BV

Print ISSN: 0898-1221


Approximation for age-structured population models using projection methods
  • Article

February 1991


33 Reads

Thomas H. Barr
"In this paper we present a class of rapidly convergent numerical schemes to solve the Sharpe-Lotka model equation from age-dependent population dynamics. This work is based on spline approximation techniques described by Banks and Kappel for functional differential equations. We provide a motivation for and description of a generalized problem which under suitable conditions is equivalent to the Sharpe-Lotka problem, we describe approximation in general which exploits the Hilbert space structure in which the generalized problem is set, and for a particular space of approximating functions we obtain estimates on the rates of convergence."

Lattice-Boltzmann simulation of blood flow in digitized vessel networks

May 2008


86 Reads

Efficient flow of red blood cells (RBCs) and white blood cells (WBCs) through the microcirculation is necessary for oxygen and nutrient delivery as well as immune cell function. Because blood is a dense particulate suspension, consisting of 40% RBCs by volume, it is difficult to analyze the physical mechanisms by which individual blood cells contribute to the bulk flow properties of blood. Both experimental and computational approaches are hindered by these non-Newtonian properties, and predicting macroscopic blood flow characteristics such as viscosity has historically been an empirical process. In order to examine the effect of the individual cells on macroscopic blood rheology, we developed a lattice Boltzmann model that considers the blood as a suspension of particles in plasma, accounting explicitly for cell-cell and cell-wall interactions. Previous studies have concluded that the abundance of leukocyte rolling in postcapillary venules is due to interactions between red blood cells and leukocytes as they enter postcapillary expansions. Similar fluid dynamics may be involved in the initiation of rolling at branch points, a phenomenon linked to atherosclerosis. The lattice Boltzmann approach is used to analyze the interactions of red and white blood cells as they flow through vascular networks digitized from normal and tumor tissue. A major advantage of the lattice-Boltzmann method is the ability to simulate particulate flow dynamically and in any geometry. Using this approach, we can accurately determine RBC-WBC forces, particle trajectories, the pressure changes in each segment that accompany cellular traffic in the network, and the forces felt by the vessel wall at any location. In this technique, intravital imaging using vascular contrast agents produces the network outline that is fed to the lattice-Boltzmann model. This powerful and flexible model can be used to predict blood flow properties in any vessel geometry and with any blood composition.

Correlation Structure of Fractional Pearson Diffusions
  • Article
  • Full-text available

September 2013


81 Reads

The stochastic solution to a diffusion equations with polynomial coefficients is called a Pearson diffusion. If the first time derivative is replaced by a Caputo fractional derivative of order less than one, the stochastic solution is called a fractional Pearson diffusion. This paper develops an explicit formula for the covariance function of a fractional Pearson diffusion in steady state, in terms of Mittag-Leffler functions. That formula shows that fractional Pearson diffusions are long range dependent, with a correlation that falls off like a power law, whose exponent equals the order of the fractional derivative.

Terminal-pair reliability in ATM virtual path networks

December 1997


33 Reads

Terminal-pair reliability (TR) in an asynchronous transfer mode (ATM) virtual path (VP) network corresponds to probabilistic quantization of robustness between two VP terminators, given a VP layout and failure probabilities of physical links. Existing TR algorithms are not viable for ATM VP networks owing to either high complexity or failure dependency among the VPs. The paper proposes two efficient algorithms for TR computation between two VP terminators by means of variants of path-based and cut-based partition methods which have been effectively used for TR computation in traditional networks. The first variant, called the path-based virtual path reliability (PVPR) algorithm, partitions the search space based on a physical path embedding the shortest route of VPs from the source to the destination terminator. The second variant, called the cut-based virtual path reliability (CVPR) algorithm, in lieu, performs the partition on the basis of a physical cutset separating the source from the remaining terminators. In both algorithms, each subproblem is recursively processed by means of partition until the source and destination terminators are contracted or disconnected. Experimental results reveal that, CVPR outperforms PVPR with respect to computation time. Moreover, compared to one of the most promising TR algorithms, both CVPR and PVPR exhibit superior performance. The two algorithms and their promising results consequently facilitate the real-time computation of the reliability or robustness of ATM VP networks

A Multi-view Approach to Semi-supervised Document Classification with Incremental Naïve Bayes

September 2007


34 Reads

Many semi-supervised learning algorithms only consider the distribution of words frequency, ignoring the semantic and syntactic information underlying the documents. In this paper, we present a new multi-view approach for semi-supervised document classification by incorporating both semantic and syntactic information. For this purpose, a co-training style algorithm Co-features is proposed, in active querying, we assign a weight to each sample according to its uncertainty factor, the most informative samples are selected and labeled by other "teachers". In contrast to batch training mode, an incremental Naive Bayes update method is realized, which allow more efficient classifier training even with large pool of unlabeled data. Experimental results show that our algorithm works successfully on Reuters-21578 and WebKB, and is superior to Co-testing in the learning efficiency.

Optimal computation of shortest paths on doubly convex bipartitegraphs

January 1998


19 Reads

An optimal parallel algorithm for computing all-pair shortest paths on doubly convex bipartite graphs is presented here. Our parallel algorithm runs in O(log n) time with O(n<sup>2</sup>/log n) processors on an EREW PRAM and is time-and-work-optimal. As a by-product, we show that the problem can be solved by a sequential algorithm in O(n<sup>2 </sup>) time optimally on any adjacency list or matrix representing a doubly convex bipartite graph. The result in this paper improves a recent work on the problem for bipartite permutation graphs, which are properly contained in doubly convex bipartite graphs

Cluster validity for fuzzy criterion clustering

November 1995


22 Reads

Defines a validity measure for fuzzy criterion clustering which is a novel approach to fuzzy clustering that in addition to being non-distance based addresses the cluster validity problem. The model is then recast as a bilevel fuzzy criterion clustering problem. The authors propose an algorithm for this model that solves both the validity and clustering problems. The authors' approach is validated via some sample problems

Synchronization paradigm for protocol testing under multi-party configuration

February 1998


6 Reads

Protocol testing leads to the synchronization problem should test sequences be applied to multiple distanced testers, namely under the multi-party configuration. This paper presents a novel synchronization paradigm which seamlessly unifies two synchronization techniques, self-synchronizable sequences and external synchronization operations. To demonstrate the viability of the proposed paradigm, we present the generations of two synchronizable sequences: the synchronizable preamble, and the synchronizable distinguishing sequences. The paper shows that the complexities of the two sequences generations are polynomial-bounded

Table 2 . Comparison of the two methods
New Lagrangian function for nonconvex primal-dual decomposition

December 1987


48 Reads

In this short paper, a new Lagrangian function is reported which is particularly suited for large-scale nonconvex optimization problems with separable structure Our modification convexifies the standard Lagrangian function without destroying its separable structure so that the primal-dual decomposition technique can be applied even to nonconvex optimization problems. Furthermore, the proposed Lagrangian results in two levels of iterative optimization as compared with the three levels needed for techniques recently proposed for nonconvex primal-dual decomposition.

Mathematical modelling of electromagnetic scattering problems

July 1998


16 Reads

We consider a wide range of electromagnetic problems of scattering by locally inhomogeneous bodies, whose dielectric and magnetic properties are characterized by arbitrary distributed tensors εˆ(x) and μˆ(x). To simulate the problems, we use singular integral equations over the domain Q of nonhomogeneity. Both 2D and 3D are examined in the same manner that includes an integral formulation of the problem, investigation of the solvability and uniqueness of the solution, an iterative numerical method. While 3D problems are formulated by a general equation, different integral equations can be considered for inhomogeneous 2D problems, depending on properties of the media and source field polarization

A new Gaussian elimination-based algorithm for parallel solution of linear equations

September 1994


33 Reads

A variant of Gaussian elimination (GE) method called the successive Gaussian elimination (SGE) algorithm, for the parallel solution of linear equations, is presented. Unlike the conventional GE algorithm, the SGE algorithm does not have a separate back-substitution phase-which requires O(N) steps using O(N) processors or O(log<sub>2 </sub><sup>2</sup>N) steps using O(N<sup>3</sup>) processors-for solving a system of N linear algebraic equations. The SGE algorithm replaces the back-substitution phase by only one step-division-and possesses numerical stability through partial pivoting. Finally, an efficient scheduling scheme for assigning the computational tasks in the SGE algorithm on to the processors in a multiprocessor system is given

Corless, R. M. What good are numerical simulations of chaotic dynamical systems? Comput. Math. Appl. 28, 107-121

November 1994


60 Reads

Numerical simulations of mathematical models can suggest that the models are chaotic. For example, one can compute an orbit and its associated finite-time Lyapunov exponents, and these computed exponents can be positive. It is not clear how far these suggestions can be trusted, because, as is well known, numerical methods can introduce spurious chaos or even suppress actual chaos. This focused review examines the fidelity of numerical methods. We look at the didactic example of the Gauss map from the theory of continued fractions, which allows a simple examination of backward error analysis for discrete dynamical systems and gives a clear picture of the effects of floating-point arithmetic. A similar use of backward error analysis, in the form of defect control, gives a useful understanding in the case of continuous dynamical systems. Finally, we discuss limitations of this ‘backward’ point of view.

Odibat, Z.M.: Analytic study on linear systems of fractional differential equations. Comput. Math. Appl. 59, 1171-1183

February 2010


434 Reads

An analytic study on linear systems of fractional differential equations with constant coefficients is presented. We briefly describe the issues of existence, uniqueness and stability of the solutions for two classes of linear fractional differential systems. This paper deals with systems of differential equations of fractional order, where the orders are equal to real number or rational numbers between zero and one. Exact solutions for initial value problems of linear fractional differential systems are analytically derived. Existence and uniqueness results are proved for two classes. The presented results are illustrated by analyzing some examples to demonstrate the effectiveness of the presented analytical approaches.

Optimal Forecasting of Discrete Stock and Flow Data Generated by a Higher Order Continuous Time System. Computers and Mathematics with Applications, 17, 1203-1214

December 1989


10 Reads

This paper is concerned with the development of an algorithm for forecasting discrete stock and flow data generated by a higher order continuous time system from a sample of stock and flow data. The algorithm is shown to be optimal in the sense that the forecasts are exact maximum likelihood estimates of the conditional expectations of the post sample observations, conditional on all the information in the sample, when the innovations are Gaussian. It is also highly efficient computationally when used in conjunction with recently developed estimation methods.

Madych, W.D.: Miscellaneous error bounds for multiquadric and related interpolators. Comput. Math. Appl. 24, 121-138

December 1992


33 Reads

We establish several types of a a priori error bounds for multiquadric and related interpolators. The results are stated and proven in the general multivariate case. These estimates show, for example, that in many cases such interpolators converge very quickly and can be used in the recovery of band limited functions from discrete data. We also include numerical experiments which illustrate the theoretical results.

Enigma 1225: Prolog-assisted solution of a puzzle using Discrete Mathematics

August 2006


168 Reads

A mathematical puzzle from a recent issue of the New Scientist magazine is solved by combining the theory of permutations with Prolog's symbolic and other computational facilities. The scheme studied is interesting because it shows that the power of the generate-and-test approach, a rather crude approach known from Artificial Intelligence, is greatly enhanced if it is supplemented by some topical knowledge from the field of study. The puzzle involves searching for matrices with certain patterns, leading to the study of permutation types. The suggested route allows for the solution of a generalized version of the original puzzle.

A constraint-based approach to Enigma 1225

October 2009


101 Reads

This paper presents a constraint programming approach to the Enigma 1225, a mathematical puzzle published in the New Scientist magazine in February 2003. An approach based on Prolog was published recently. In this paper we give a constraint programming perspective on the problem, highlighting the differences between the two methodologies. We show how problem-specific knowledge can be easily incorporated into a constraint-based approach, giving an efficient constraint model for the generalized version of the puzzle. From the constraint programming point of view, the Enigma 1225 puzzle exhibits interesting symmetries, that can be eliminated using only a small number of constraints added to the model. Furthermore, properties of the puzzle can be used to derive a strong constraint propagation scheme that limits the search once an optimal solution has been found.

Counting linear extension majority cycles in partially ordered sets on up to 13 elements

February 2010


30 Reads

It is well known that the linear extension majority relation of a partially ordered set (P,≤P) can contain cycles when at least 9 elements are present in P. Computer experiments have uncovered all posets with 9 elements containing such cycles and limited frequency estimates for linear extension majority cycles (or LEM cycles) in posets on up to 12 elements are available. In this contribution, we present an efficient approach which allows us to count and store all posets containing LEM cycles on up to 13 elements.

Chang, P.C.: A Branch and Bound Approach for Single Machine Scheduling with Earliness and Tardiness Penalties. Computers and Mathematics with Applications 37, 133-144

May 1999


53 Reads

An n job, single machine scheduling problem in which each job has a distinct due date, di, is studied in this paper. The objective is to determine an optimal schedule π0s for a set of jobs, S, such that the total absolute deviation of the schedule is minimized. This objective function is based on the due date value and on the earliness or tardiness of each job in the selected sequence. This paper presents a bounding scheme for the calculation of different lower bounds based on the overlap elimination procedure on a Just-In-Time schedule. Properties and theorems of the overlap elimination procedure are also provided. Finally, a numerical example is illustrated and some extensions of the approach are also discussed.

Comment on 'Comment on: "Application of an adaptive neural fuzzy inference system to thermal comfort and group technology problems" (vol 54, pg 1395, 2007)

December 2007


62 Reads

The Adaptive Neural Fuzzy Inference System (ANFIS) is used to design two vague systems, namely thermal comfort and group technologies in production and operations management. Results show that both systems can be modeled successfully by the combined use of a fuzzy approach and neural network learning.

14-velocity and 18-velocity multiple-relaxation-time lattice Boltzmann models for three-dimensional incompressible flows

March 2015


111 Reads

In this paper, 14-velocity and 18-velocity multiple-relaxation-time (MRT) lattice Boltzmann (LB) models are proposed for three-dimensional incompressible flows. These two models are constructed based on the incompressible LBGK model proposed by He et al. (Chin. Phys., 2004, 13: 40-46) and the MRT LB model proposed by d'Humi\`{e}res et al. (Philos. Trans. R. Soc., A, 2002, 360: 437-451), which have advantages in the computational efficiency and stability, respectively. Through the Chapman-Enskog analysis, the models can recover to three-dimensional incompressible Navier-Stokes equations in the low Mach number limit. To verify the present models, the steady Poiseuille flow, unsteady pulsatile flow and lid-driven cavity flow in three dimensions are simulated. The simulation results agree well with the analytical solutions or the existing numerical results. Moreover, it is found that the present models show higher accuracy than d'Humi\`{e}res et al. model and better stability than He et al. model.

Wood G.R.: Multidimensional bisection applied to global optimisation. Comput. Math. Appl. 21, 161-172

December 1991


49 Reads

A family of deterministic algorithms is introduced, designed to solve the global optimisation problem for Lipschitz continuous functions of many variables. All the algorithms can be considered as generalisations of the bisection method: they proceed via a sequence of brackets whose infinite intersection is the set of global optima. Brackets are unions of similar simplexes. Acceleration methods, convergence properties and optimality questions are considered.

An 18 GFLOPS parallel climate data assimilation PSAS package

December 1996


22 Reads

We have designed and implemented a set of highly efficient and highly scalable algorithms for an unstructured computational package, the PSAS data simulation package, as demonstrated by detailed performance analysis of systematic runs up to 512 nodes of an Intel Paragon. The preconditioned Conjugate Gradient solver achieves a sustained 18 Gflops performance. Consequently, we achieve an unprecedented 100-fold reduction in time to solution on the Intel Paragon over a single head of a Cray C90. This not only exceeds the daily performance requirement of the Data Assimilation Office at NASA's Goddard Space Flight Center, but also makes it possible to explore much larger and challenging data assimilation problems which are unthinkable on a traditional computer platform such as the Cray C90.

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